This paper is devoted to the study of some asymptotic properties of a -estimator in a framework of detection of abrupt changes in random field’s distribution. This class of problems includes e.g. recovery of sets. It involves various techniques, including -estimation method, concentration inequalities, maximal inequalities for dependent random variables and -mixing. Penalization of the criterion function when the size of the true model is unknown is performed. All the results apply under mild, discussed assumptions. Simple examples are provided.
Mots-clés : detection of change-points, $M$-estimation, penalized $M$-estimation, concentration inequalities, maximal inequalities, mixing
@article{PS_2002__6__189_0,
author = {Chambaz, Antoine},
title = {Detecting abrupt changes in random fields},
journal = {ESAIM: Probability and Statistics},
pages = {189--209},
publisher = {EDP-Sciences},
volume = {6},
year = {2002},
doi = {10.1051/ps:2002011},
mrnumber = {1943147},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ps:2002011/}
}
Chambaz, Antoine. Detecting abrupt changes in random fields. ESAIM: Probability and Statistics, Tome 6 (2002), pp. 189-209. doi : 10.1051/ps:2002011. http://archive.numdam.org/articles/10.1051/ps:2002011/
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